Modeling the infrared interstellar extinction

Planetary and Space Science ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Modeling the infrared interstellar extinction Shu Wang a,b,n, Aigen Li b,n, B.W. Jiang a,b,n a b

Department of Astronomy, Beijing Normal University, Beijing 100875, China Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 11 November 2013 Received in revised form 21 March 2014 Accepted 24 March 2014

How dust scatters and absorbs starlight in the interstellar medium (ISM) contains important clues about the size and composition of interstellar dust. While the ultraviolet (UV) and visible interstellar extinction is well studied and can be closely fitted in terms of various dust mixtures (e.g., the silicate–graphite mixture), the infrared (IR) extinction is not well understood, particularly, the mid-IR extinction in the 3–8 μm wavelength range is rather flat (or “gray”) and is inconsistent with the standard Mathis, Rumpl, & Nordsieck (MRN) silicate–graphite dust model. We attempt to reproduce the flat IR extinction by exploring various dust sizes and species, including amorphous silicate, graphite, amorphous carbon and iron. We find that the flat IR extinction is best explained in terms of micrometer-sized amorphous carbon dust which consumes
60 carbon atoms per million hydrogen atoms (i.e., C/H E60 ppm). To account for the observed UV/visible and near-IR extinction, the silicate–graphite model requires Si/H E34 ppm and C/HE 292 ppm. We conclude that the extinction from the UV to the mid-IR could be closely reproduced by a mixture of submicrometer-sized amorphous silicate dust, submicrometer-sized graphitic dust, and micrometer-sized amorphous carbon dust, at the expense of excess C available in the ISM (i.e., this model requires a solid-phase C abundance of C/H E 352 ppm, considerably exceeding what could be available in the ISM). & 2014 Elsevier Ltd. All rights reserved.

Keywords: Infrared Extinction Dust Model

1. Introduction The interstellar extinction is one of the primary sources of information about the interstellar dust size and composition. The interstellar extinction varies from one sightline to another in the ultraviolet (UV) and the optical wavelength range. This variation in the Milky Way galaxy can be described by a single parameter, i.e., RV (Cardelli et al., 1989; hereafter CCM).1 The average extinction law for the Galactic diffuse interstellar medium (ISM) corresponds to RV  3:1. Based on the interstellar extinction curve observed for the diffuse ISM RV  3:1, Mathis et al. (1977) constructed a simple interstellar dust model to fit the interstellar extinction observed over the wavelength range of 0:11 μm o λ o 1 μm. This classic model – known as the “MRN” model – consists of silicate and graphite grains2

n

Corresponding authors. E-mail addresses: [email protected] (S. Wang), [email protected] (A. Li), [email protected] (B.W. Jiang). 1 RV  AV =EðB  V Þ is the total-to-selective extinction ratio, where EðB V Þ  AB  AV is the reddening which is the difference between the extinction in the blue band (AB) and the extinction in the visual band (AV). 2 Hoyle and Wickramasinghe (1962) first proposed that graphite grains of sizes a few times 0.01 μm could condense in the atmospheres of cool N-type carbon stars, and these grains would subsequently be driven out of the stellar atmospheres and injected into the interstellar space by the stellar radiation pressure. Similarly,

and takes a simple power-law size distribution dn=da p a  α with α  3:5 for the size range of 50 Å o a o 0:25 μm, where a is the radius of the dust which is assumed to be spherical.3 This model was

(footnote continued) Kamijo (1963) suggested that nanometer-sized SiO2 grains could condense in the atmospheres of cool M-type stars. Gilman (1969) argued that grains around oxygen-rich cool giants could mainly be silicates such as Al2SiO5 and Mg2SiO4. Silicates were first detected in emission in M stars (Woolf and Ney, 1969; Knacke et al., 1969). After blown out of the stellar atmospheres and injected into the interstellar space, silicates could become an interstellar dust component. Hoyle and Wickramasinghe (1969) first modeled the interstellar extinction in terms of a mixture of silicate grains of radii
0.07 μm and graphite grains of radii
0.065 μm. Wickramasinghe and Nandy (1970) found that a mixture of silicate, graphite, and iron grains achieved a rough fair fit to the interstellar extinction curve 1 at λ o 8 μm  1 . 3 To be precise, the MRN model actually derived a wider size range of 50 Å o ao 1 μm for the graphite component and a narrower size range of 0:025 μm o a o 0:25 μm for the silicate component (and for other components such as SiC, iron and magnetite), with α E 3.3–3.6. In the literature, the MRN model is customarily taken to be a mixture of silicate and graphite with α ¼3.5 and 50 Å o a o 0:25 μm. This is probably because (1) in their Fig. 4 the demonstrated model fit to the observed UV/visible extinction was provided by the olivine– graphite mixture with α ¼3.5 and 50 Å o a o 0:25 μm for both dust components; and (2) Draine and Lee (1984) also derived α ¼ 3.5 and 50 Å o a o 0:25 μm for both dust components using improved optical constants for these two substances. The sudden cutoff at amin ¼ 50 Å and amax ¼ 0:25 μm is not physical. Kim et al. (1994) and WD01 adopted a more smooth size distribution function which extends

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Fig. 1. Comparison of the IR extinction observed for various interstellar regions with that predicted from the MRN (red dot-dashed line) and WD01 (black solid line) silicate–graphite models for the diffuse ISM of which the UV/optical extinction is characterized by RV  3:1. The little bump at 6.2 μm arises from the C–C stretching absorption band of PAHs (see Li and Draine, 2001). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

further developed by Draine and Lee (1984) who extensively discussed the optical properties of “astronomical” silicate and graphite materials. Subsequent developments were made by Draine and his coworkers (Weingartner and Draine, 2001 [hereafter WD01], Li and Draine, 2001) who extended the silicate–graphite grain model to explicitly include polycyclic aromatic hydrocarbon (PAH) molecules to explain the so-called “unidentified infrared emission” (UIE) bands at 3.3, 6.2, 7.7, 8.6, and 11.3 μm (see Léger and Puget, 1984; Allamandola et al., 1985). With the wealth of available data from space-borne telescopes (e.g., Infrared Space Observatory [ISO] and Spitzer Space Telescope) and ground-based surveys (e.g., Two Micron All Sky Survey [2MASS]) in the near- and mid-infrared, in recent years we have seen an increase in interest in the infrared (IR) extinction. Understanding the effects of dust extinction in the IR wavelengths is important to properly interpret these observations. While the UV/ optical extinction has been extensively observed for a wide variety of environments and modeled in terms of various dust models, our understanding of the near- and mid-IR extinction is still somewhat poor and controversial, despite that in this spectral domain many advances have been made in the past few years (see Section 1 of Wang et al., 2013). As shown in Fig. 1, WD01 silicate–graphite grain model predicts  1:74 a power-law of Aλ p λ for the IR extinction at 1 μm o λ o 7 μm, while the MRN model predicts a steeper power-law of  2:02 4 Aλ p λ . The model IR extinction curves reach their minimum at
7 μm where the extinction power-law intersects the bluewing of the 9.7 μm silicate absorption band. Rieke and Lebofsky (1985) measured the IR extinction from 1 μm to 13 μm for the lines of sight toward o Sco, a normal A5 II star behind the edge of the ρ Oph cloud obscured by AV  2:92 mag,5 and toward a number of stars in the galactic center (GC). Rieke and Lebofsky (1985) derived a power-law of

(footnote continued) smoothly to a 4 1 μm. But the dust with a 41 μm takes only a negligible fraction of the total dust mass.

4 At λ 47 μm, the extinction increases because of the 9.7 μm silicate Si–O stretching absorption band. 5 The extinction toward o Sco at λ 40:55 μm can be well described by the RV ¼ 3.1 extinction law. At λ o 0:55 μm, the observed colors of o Sco are much bluer than expected from those of a normal A5 II star obscured by AV ¼ 2:92 mag with

Aλ p λ for 1 μm o λ o 7 μm for o Sco and the GC sources. Draine (1989) compiled the IR extinction observed for a range of galactic regions including diffuse clouds, molecular clouds,  1:75 and HII regions. He derived a power-law of Aλ p λ for 1 μm o λ o 7 μm. More recently, Bertoldi et al. (1999) and Rosenthal et al. (2000) also derived a power-law extinction of  1:7 Aλ p λ for 2 μm o λ o 7 μm for the Orion molecular cloud (OMC).6 However, numerous recent observations suggest the mid-IR extinction at 3 μm o λ o 8 μm to be almost universally flat or “gray” for both diffuse and dense environments (see Section 1.4 of Wang et al., 2013 for a summary), much flatter than that predicted from the MRN or WD01 silicate–graphite model for RV ¼3.1 (see Fig. 1). Lutz et al. (1996) derived the extinction toward the GC star Sgr An between 2.5 μm and 9 μm from the H recombination lines. They found that the GC extinction shows a flattening of Aλ in the wavelength region of 3 μm o λ o9 μm, clearly lacking the pronounced dip at
7 μm predicted from the RV ¼3.1 silicate– graphite model (see Fig. 1). This was later confirmed by Lutz (1999), Nishiyama et al. (2009), and Fritz et al. (2011). Indebetouw et al. (2005) used the photometric data from the 2MASS survey and the Spitzer/GLIMPSE Legacy program to determine the IR extinction. From the color excesses of background stars, they derived the
1.25–8 μm extinction laws for two very different lines of sight in the Galactic plane: the l ¼421 sightline toward a relatively quiescent region, and the l¼ 2841 sightline which crosses the Carina Arm and contains RCW 49, a massive star-forming region. The extinction laws derived for these two distinct Galactic plane fields are remarkably similar: both show a flattening across the 3–8 μm wavelength range, consistent with that derived by Lutz et al. (1996) for the GC. Jiang et al. (2006) derived the extinction at 7 and 15 μm for more than 120 sightlines in the inner Galactic plane based on the ISOGAL survey data and the near-IR data from DENIS and 2MASS, using RGB tip stars or early AGB stars (which have only moderate mass loss) as the extinction tracers. They found the extinction well exceeding that predicted from the MRN or WD01 RV ¼3.1 model. Flaherty et al. (2007) obtained the mid-IR extinction laws in the Spitzer/IRAC bands for five nearby star-forming regions. The derived extinction laws at
4–8 μm are flat, even flatter than that of Indebetouw et al. (2005). Gao et al. (2009) used the 2MASS and Spitzer/GLIPMSE data to derive the extinction in the four IRAC bands for 131 GLIPMSE fields along the Galactic plane within jljr 65o . Using red giants and red clump giants as tracers, they also found the mean extinction in the IRAC bands to be flat. Wang et al. (2013) determined the mid-IR extinction in the four Spitzer/IRAC bands of five individual regions in Coalsack, a nearby starless dark cloud, spanning a wide variety of interstellar environments from diffuse and translucent to dense clouds. They found that all regions exhibit a flat mid-IR extinction. All these observations appear to suggest a “universally” flat extinction law in the mid-IR, with little dependence on environments.7 While rapid progress has been made in observationally determining the mid-IR extinction and numerous IR extinction

(footnote continued) the RV ¼ 3.1 extinction law, leading to the assignment of RV  4:0 (see Rieke and Lebofsky, 1985). 6 The OMC extinction also displays an absorption band at 3.05 μm attributed to water ice. 7 We should note that an “universally” flat mid-IR extinction law does not necessarily mean an identical mid-IR extinction law for all regions, instead, it merely means a flattening trend of Aλ with λ in the mid-IR. Chapman et al. (2009), McClure (2009), and Cambrésy et al. (2011) found that the shape of the mid-IR extinction law appears to vary with the total dust extinction. But also see Román-

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curves have been accumulated both for the Milky Way and for the Magellanic Clouds (e.g., see Gao et al., 2013a), theoretical understanding of the nature and origin of the flat mid-IR extinction lags well behind the observations. We plan to model the interstellar extinction from the far-UV to the far-IR for a wide range of interstellar environments. In this work we present our first attempts to understand the nature of the flat mid-IR extinction. In Section 2 we summarize the current status in interpreting the flat mid-IR extinction. Section 3 describes our model. Section 4 presents the results and discussions.

2. Modeling the mid-IR extinction: where do we stand? To the best of our knowledge, only WD01 and Dwek (2004) have closely reproduced the flat mid-IR extinction. Using a mixture of amorphous silicate dust and carbonaceous dust,8 WD01 fitted the UV/ optical and near-IR extinction curves of different values of RV in the wavelength range of 0:125 μm o λ o 2:86 μm. Draine (2003) extended the WD01 model of RV ¼5.5 into the IR up to λ o 30 μm. It is amazing that the WD01 RV ¼5.5 model closely reproduces the flat mid-IR extinction observed toward the GC (Lutz et al., 1996; also see Fig. 2). The success of the WD01 RV ¼5.5 model and the failure of the WD01 RV ¼ 3.1 model in fitting the flat mid-IR extinction suggest that the flat mid-IR extinction implies a population of large dust, although the exact size and the quantity of this dust population are not known. Generally speaking, denser regions tend to have flatter extinction curves in the UV and higher values RV: increased RV is attributed to tilt in size distribution to decrease numbers of small grains, and increase numbers of large grains due to grain growth primarily through coagulation (Draine, 2011). However, the flat mid-IR extinction is not only seen in dense regions but, as discussed in Section 1, the flat mid-IR extinction has also been seen in various interstellar environments, including diffuse clouds (e.g., the low-density lines of sight in the Galactic midplane [see Zasowski et al., 2009], and the diffuse and translucent regions of the Coalsack nebula [see Wang et al., 2013]). The RV ¼5.5 size distribution is more appropriate for dense regions. Dwek (2004) hypothesized that metallic needles may play an important role in accounting for the flat mid-IR extinction. As shown in Fig. 2, Dwek (2004) argued that, combined with the silicate–graphite mixture for the RV ¼ 3.1 model (Zubko et al., 2004), metallic needles9 with a typical length (l) over radius (a) ratio of l=a  600 and a needle-to-H mass ratio of
5  10  6 could explain the flat mid-IR extinction derived by Lutz (1999) for the GC. However, it is not clear if metallic needles are indeed present in the ISM (see Li, 2003). It would be interesting to study their generation and evolution in the ISM and their optical properties. Gao et al. (2013b) have also attempted to fit the
1–19 μm IR extinction curve toward the GC derived by Fritz et al. (2011). Their best-fit model for the GC IR extinction constrains the visual extinction to be AV
38–42 mag. But their model could not simultaneously reproduce both the relatively steep
1–3 μm near-IR extinction and the flat
3–8 μm mid-IR extinction. They suggested that the extinction toward the GC could be due to a

Fig. 2. Comparison of the IR extinction observed for various interstellar regions with that predicted from the WD01 model for RV ¼5.5 (black solid line) and the iron needle model (red dot-dashed line) of Dwek (2004) which is a combination of the RV ¼ 3.1 silicate–graphite model of Zubko et al. (2004, green dashed line) and iron needles (blue dashed line). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

combination of dust in different environments: dust in diffuse regions (characterized by small RV and steep near-IR extinction), and dust in dense regions (characterized by large RV and flat UV extinction).

3. Our model We aim at simultaneously reproducing the observed UV/optical and near- and mid-IR extinction. Following MRN and WD01, we assume a mixture of amorphous silicate dust and graphite dust. The optical constants of amorphous silicate dust and graphitic dust are taken from Draine and Lee (1984). Since the flat mid-IR extinction is seen both in diffuse clouds and in dense clouds, we consider the UV/optical and near-IR extinction curves of different RV values: RV ¼3.1, 4.0, and 5.5. We adopt an exponentially cutoff power-law size distribution for both dust components: dn=da p a  α expð  a=ac Þ for amin o a o amax , where a is the spherical radius of the dust (we assume the dust to be spherical), α is the power exponent, and ac is the cutoff size. Following MRN, the lower cutoff of the dust size is initially taken to be amin ¼ 50 Å. But for the RV ¼ 4:0; 5:5 curves, we find that amin ¼ 25 Å is more favorable. The upper cutoff is set at amax ¼ 2:5 μm. We have five parameters: αS and ac;S for the silicate component, αC and ac;C for the carbonaceous component (i.e., graphite), and f C2S , the mass ratio of graphite to silicate dust. The ratio of the total model extinction at wavelength λ to the column density of H nuclei is calculated from Aλ =N H ¼ 1:086 N 0S  C ext ðλÞ; Z

C ext ðλÞ ¼ (footnote continued) Zúñiga et al. (2007) and Ascenso et al. (2013) who found no evidence for the dependence of the mid-IR extinction law on the total dust extinction. 8 The carbonaceous grain population was assumed to extend from grains with graphitic properties at radii a 40:01 μm, down to particles with PAH-like properties at very small sizes (see Li and Draine, 2001). 9 The idea of metallic needles was originally brought up by Hoyle et al. (1968) and Wickramasinghe et al. (1975) to explain the 2.7 K cosmic microwave background (CMB). They argued that the 2.7 K CMB might have arisen from the radiation of “Population III” objects thermalized by long slender conducting cosmic whiskers or “cosmic needles”.

amax amin

C ext;S ða; λÞa  αS expð  a=ac;S Þ da

þ ðN 0C =N 0S Þ N obs

N0S ¼ ∑

j¼1

"

n

ð1Þ

Z

amax

amin

C ext;C ða; λÞa  αC expð  a=ac;C Þ da;

ðAλ =NH Þobs;j  C ext ðλj Þ=s2obs;j Nobs

= 1:086 ∑ fC ext ðλj Þ=sobs;j g j¼1

ð2Þ

o

# 2

;

ð3Þ

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N 0C =N 0S ¼ f C2S  ðρS =ρC Þ  Z =

amax

Z

amax

a3  αS expð a=ac;S Þ da

amin

a3  αC expð  a=ac;C Þ da;

ð4Þ

amin

where N 0S and N 0C are respectively proportional to the column densities of the silicate and graphite dust, ρS ¼ 3:5 g cm  3 and ρC ¼ 2:24 g cm  3 are respectively the mass densities of the silicate and the graphite dust, C ext;S ða; λÞ and C ext;C ða; λÞ are respectively the extinction cross sections of the silicate and the graphite dust of size a at wavelength λ, C ext ðλÞ is the extinction at wavelength λ of the silicate–graphite mixture per silicate dust column, and ðAλ =N H Þobs;j and sobs;j are respectively the “observed” extinction and uncertainty at wavelength λj. For the UV/optical and near-IR extinction, we follow WD01 to fit the CCM extinction characterized by RV between 0.35 and 8 μm  1 and evaluate the extinction at Nobs ¼100 wavelengths λj, equally spaced in ln λ. As will be shown later in Section 4, although this simple grain model could closely reproduce the observed UV/optical and nearIR extinction, it could not fit the flat mid-IR extinction. Guided by the fact that dust scatters and absorbs starlight most effectively at wavelengths comparable to its size (i.e., 2π a=λ
1; see Wang et al., 2014), we will add an extra population of large, micrometer-sized dust to account for the flat mid-IR extinction. For this large, micrometer-sized dust population, we will consider amorphous silicate, graphite, amorphous carbon, and metallic iron. We adopt the optical constants of the “ACAR”-type amorphous carbon of Rouleau and Martin (1991). The optical constants of iron are taken from Li (2003). For the mid-IR extinction, we compare the model results with the observational data for the following regions as a whole: the Galactic center (Lutz, 1999; Nishiyama et al., 2009), the Galactic plane (Indebetouw et al., 2005; Jiang et al., 2006; Gao et al., 2009), nearby star-forming regions (Flaherty et al., 2007), and the Coalsack nebula (Wang et al., 2013). Ideally, the CCM UV/optical extinction should be combined only with the IR extinction for the regions characterized by the same RV. However, the regions for which the mid-IR extinction has been measured are not well characterized and their RV values are not well determined.10 Nonetheless, as illustrated in Fig. 1, the mid-IR extinction for different regions does not appear to differ substantially from each other and on average, a flat mid-IR extinction is well established. It is interesting to note that, as shown in Wang et al. (2013) for the Coalsack nebula, the mid-IR extinction of diffuse regions seems to be even somewhat flatter than that of dense regions. Therefore, we intend to compare our model results with the mid-IR observations as a whole, instead of an individual region. In modeling the UV/optical extinction, we perform a gridsearch by minimizing χ2 (see Eq. 8 of WD01) with the weights given by WD01. We fit the mid-IR extinction by eye as we do not know how the mid-IR extinction data points should be weighted compared to the UV/optical extinction. We fit the UV/optical segment and the mid-IR segment separately but requiring that the addition of the mid-IR model extinction to the total extinction does not distort the fit to the UV/optical part.

10 For example, the line of sight toward the Galactic center is often considered as a sightline of diffuse clouds as revealed by the presence of the 3.4 μm C–H aliphatic hydrocarbon stretching absorption feature which is not seen in molecular clouds (Pendleton and Allamandola, 2002; Mennella et al., 2002). However, the Galactic center sightline must also contain molecular cloud materials as revealed by the presence of the 3.1 μm and 6.0 μm H2O ice absorption features (e.g., see McFadzean et al., 1989).

Fig. 3. Fitting the RV ¼3.1 UV/optical and near-IR extinction with a simple mixture (black solid line) of amorphous silicate (green dashed line) and graphite dust (blue dashed line). The black solid line plots the model fit, while the red solid line plots the RV ¼3.1 extinction curve observed for diffuse regions. See Section 3 for details. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

4. Results and discussion To testify our model, we first fit the UV/optical and the near-IR extinction curve of RV ¼3.1. We assume that silicate and graphite have the same size distribution (i.e., αS ¼ αC , ac;S ¼ ac;C ). Fig. 3 shows the best-fit results. The best-fit model parameters are listed in Table 1. The abundances of the dust-forming heavy elements locked up in the dust can be derived from the following equation: ½X=H ¼ 4π =3  ρX =mH  NX =μX Z amax  N0X a3  αX expð  a=ac;X Þ da;

ð5Þ

amin

where mH ¼ 1:66  10  24 g is the mass of a hydrogen atom, ρX and N 0X are respectively the mass density and the column density of the dust species containing element X, and N X and μX are respectively the number of X atoms in and the molecular weight of a molecule of the dust species containing element X. We consider elements Si and C and dust species amorphous silicate and graphite: μC  12, NC ¼ 1, μS  172, and NSi ¼ 1.11 We derive the C and Si abundances required to be locked up in dust to be ½C=Hdust  292 ppm and ½Si=Hdust  ½Mg=Hdust  ½Fe=Hdust  34 ppm (ppm refers to “parts per million”). For the dust-forming element X, let ½X=HISM be the “interstellar abundance” – the total abundance of this element in the ISM, both in gas and in dust; and ½X=Hgas be the gas-phase abundance of this element. The abundance of this element in dust is ½X=Hdust ¼ ½X=HISM  ½X=Hgas . The gas-phase Mg, Si and Fe abundances are negligible (i.e., these rock-forming elements are almost completely depleted from the gas phase; see Li (2005) and references therein). Therefore, for Si we have ½Si=Hdust  ½Si=HISM . The interstellar abundance of Si (i.e., ½Si=HISM ) is not known. Traditionally, one often adopts the solar photospheric abundances (e.g., Asplund et al., 2009) of heavy elements as their interstellar abundances. However, Lodders (2003) argued that the currently observed solar photospheric abundances (relative to H) must be lower than those of the proto-Sun because helium and other heavy elements have settled toward the Sun's interior since the time of the Sun's formation some 4.55 Gyr ago. She further suggested that protosolar abundances derived from the photospheric abundances by considering settling effects are more representative of the solar system elemental abundances. 11

For silicate dust, we assume its chemical composition to be MgFeSiO4.

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Table 1 Model parameters for fitting the UV/optical and near-IR extinction. Extinction type

AKS =N H ð10  23 mag cm2 Þ

αS

αC

ac;S (μm)

f C2S

N 0S (cm  2)

½Si=Hdust (ppm)

RV ¼ 3.1

6.26

3.2

3.2

0.14

0.6

4:687  10  24

34.0

292

RV ¼ 4.0

6.85

2.7

2.7

0.12

0.6

1:669  10  21

30.7

264

RV ¼ 5.5

7.40

2.1

3.0

0.16

0.3

1:047  10  18

40.0

172

On the other hand, it has also been argued that the interstellar abundances might be better represented by those of B stars and young F, G stars (because of their young ages) which are just
60– 70% of the solar values (i.e., “subsolar”; Snow and Witt, 1996; Sofia and Meyer, 2001). However, Li (2005) showed that if the interstellar abundances are indeed “subsolar” like B stars and young F, G stars, there might be a lack of raw material to form the dust to account for the interstellar extinction. We also note that Przybilla et al. (2008) derived the photospheric abundances of heavy elements for six unevolved early B-type stars in the solar neighborhood OB associations and the field using NLTE techniques. They found that the photospheric abundances of those B stars are in close agreement with the solar values. Nieva and Przybilla (2012) further derived the photospheric abundances of 29 slowly rotating early B-type stars. These stars exhibit o 10% abundance fluctuations and their abundances are also similar to that of the Sun. The Si abundance of the Sun, proto-Sun, and early B stars is respectively ½Si=H   32 ppm (Asplund et al., 2009), 41 ppm (Lodders, 2003), and 32 ppm (Przybilla et al., 2008; Nieva and Przybilla, 2012). The model which best fits the UV/optical extinction requires ½Si=Hdust  34 ppm, consistent with the solar, protoSun or B stars Si abundance. For C, it is more complicated since the gas-phase C abundance is recently under debate. Earlier studies reported ½C=Hgas  140 ppm from the weak intersystem absorption transition of C II] at 2325 Å (Cardelli et al., 1996; Sofia et al., 2004). Very recently, Sofia et al. (2011) derived ½C=Hgas  100 ppm for several interstellar sightlines from the strong transition of C II] at 1334 Å. They argued that the oscillator strength for the C II] transition at 2325 Å previously used by Cardelli et al. (1996) and Sofia et al. (2004) to obtain ½C=Hgas  140 ppm might have been underestimated. The solar C abundance and proto-Sun C abundance are respectively ½C=H   224 ppm (Asplund et al., 2009) and 288 ppm (Lodders, 2003). The C abundance of the early B stars which are thought to be ideal indicators for the present-day interstellar abundances since they preserve their pristine abundances is close to the solar C abundance: ½C=H⋆  214 7 20 ppm (Przybilla et al., 2008) and ½C=H⋆  209 7 15 ppm (Nieva and Przybilla, 2012). If the interstellar C abundance is like that of the early B stars (i.e., ½C=HISM  209 ppm) or that of the proto-Sun (i.e., ½C=HISM  288 ppm),with the gas-phase C abundance of ½C=Hgas  100 ppm (Sofia et al., 2011) subtracted,there will be only
109 ppm or
188 ppm of C available to make the carbonaceous dust. However,the model which best fits the UV/optical extinction requires ½C=Hdust  292 ppm, substantially exceeding what would be available to be locked up in dust.12 As shown in Fig. 3, the silicate–graphite mixture model with ½Si=Hdust  34 ppm and ½C=Hdust  292 ppm closely reproduces the observed UV/optical/near-IR extinction. However, it fails in

12 We note that, except the composite dust model of Mathis (1996) which only requires ½C=Hdust  155 ppm (and ½Si=Hdust  31 ppm, but see Dwek, 1997), all interstellar grain models consume more C than the available value of
109 ppm or
188 ppm in the ISM: ½C=Hdust  194 ppm (and ½Si=Hdust  20 ppm) of Li and Greenberg (1997), ½C=Hdust  231 ppm (and ½Si=Hdust  48 ppm) of WD01, ½C=Hdust  244 ppm (and ½Si=Hdust  36 ppm) of Zubko et al. (2004), ½C=Hdust  233 ppm (and ½Si=Hdust  50 ppm) of Jones et al. (2013).

½C=Hdust (ppm)

fitting the flat 3–8 μm mid-IR extinction (see Fig. 4a). According to light scattering theory, dust absorbs and scatters starlight most effectively if its size is comparable to the starlight wavelength. Therefore, the dust which dominates the mid-IR extinction at
3–8 μm should be in micrometer size scale, as inferred from the consideration of a
λ=2π . This leads us to add an extra population of large, micrometer-sized dust to account for the mid-IR extinction. We explore the size of the dust ranging from a ¼0.5 μm to a¼ 3.5 μm. For simplicity, we only consider dust of single sizes. In principle, we could assume a log-normal size distribution or the WD01-type size distribution for this micrometer-sized dust population. But we do not expect that a distribution of dust sizes would affect the conclusion drawn from the single-size model. A distribution of sizes would remove the ripple structures in the extinction curve of single-sized dust. The observed mid-IR extinction is commonly derived from broad-band photometry and therefore could tolerate the wavy ripples. As shown in Fig. 4a, the RV ¼3.1 model together with spherical amorphous carbon dust of radius of a  1:5 μm and C/H E 60 ppm could closely fit the mid-IR extinction. These micrometer-sized amorphous carbon grains, with 2π a=λ b 1, are “gray” in the UV/ optical wavelength regime. Therefore, the addition of micrometersized dust does not distort the fit to the observed RV ¼ 3.1 extinction curve provided by the silicate–graphite model. In total, this model requires ½C=Hdust  352 ppm to account for the observed extinction from the UV to the mid-IR, with
17% of the C atoms locked up in the micrometer-sized amorphous carbon component. We have also considered micrometer-sized graphite, amorphous silicate, and iron dust. As shown in Fig. 4b, graphite of radius of a¼ 1.5 μm is also capable of reproducing the flat mid-IR extinction. However, the micrometer-sized graphite population requires C/H E 92 ppm. Therefore, amorphous carbon, with C/H E 60 ppm, seems more favorable since the RV ¼3.1 silicate– graphite model already encounters a “carbon crisis” problem: the model consumes more C/H than what is available. As shown in Fig. 4c, amorphous silicate could not fit the mid-IR extinction for two reasons: (1) the best-fit model with a¼ 3 μm predicts a prominent dip at λ
8 μm which is not seen in the observed mid-IR extinction; this dip is due to the onset of the 9.7 μm Si–O stretch at λ
8 μm; (2) this model requires Si/ H E 21,000 ppm to be locked up in the micrometer-sized silicate dust, which is far more than the available amount of ½Si=HISM  32–41 ppm in the ISM. Fig. 4d shows the fit obtained with Fe/H E84 ppm in iron spheres of a ¼1.5 μm. Although the fit to the mid-IR extinction is excellent, this model requires a total depletion of Fe/ HE116 ppm,13 while the Fe abundance of the Sun, proto-Sun, and early B stars is only ½Fe=H   27:5 ppm (Asplund et al., 2009), ½Fe=H   34:7 ppm (Lodders, 2003), and ½Fe=H⋆  28–33 ppm (Przybilla et al., 2008; Nieva and Przybilla, 2012) respectively. We have also considered models for the RV ¼ 4.0 and RV ¼5.5 extinction curves since the flat mid-IR extinction has also been

13 To account for the UV/optical extinction, the submicrometer-sized amorphous silicate component consumes Fe/HE 32 ppm.

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Fig. 4. Fitting the RV ¼ 3.1 UV/optical, near- and mid-IR extinction with a simple mixture (thin black solid line) of amorphous silicate (green dashed line) and graphite dust (blue dashed line), together with a population of large, micrometer-sized dust: (a) amorphous carbon of a  1:5 μm and C/H E 60 ppm, (b) graphite of a  1:5 μm and C/H E 92 ppm, (c) amorphous silicate of a  3:0 μm and Si/H E 21,000 ppm, and (d) iron of a  1:5 μm and Fe/H E 84 ppm. The thick red solid line plots the model fit, while the symbols plot the observed extinction: the magenta open triangles plot the RV ¼ 3.1 UV/optical/near-IR extinction, the other symbols plot the mid-IR extinction. See Section 4 for details. (a) Rv= 3.1 sil.+gra.+mm-sized am. car. (b) Rv= 3.1 sil.+gra.+mm-sized graphite, (c) Rv= 3.1 sil.+gra.+mm-sized sil. (d) Rv= 3.1 sil.+gra.+mm-sized iron spheres. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Fig. 5. Same as Fig. 4 but for RV ¼ 4.0. (a) Rv= 4.0 sil.+gra.+mm-sized am. car. (b) Rv= 4.0 sil.+gra.+mm-sized graphite, (c) Rv= 4.0 sil.+gra.+mm-sized sil. (d) Rv= 4.0 sil.+gra. +mm-sized iron spheres.

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Fig. 6. Same as Fig. 4 but for RV ¼ 5.5. (a) Rv= 5.5 sil.+gra.+mm-sized am. car. (b) Rv= 5.5 sil.+gra.+mm-sized graphite, (c) Rv= 5.5 sil.+gra.+mm-sized sil. (d) Rv= 5.5 sil.+gra. +mm-sized iron spheres.

seen in dense regions (see Section 2). For the RV ¼4.0 case, we also assume that both silicate and graphite have the same size distribution. The results are shown in Fig. 5 and Table 1. It is seen that both amorphous carbon of a  1:6 μm and graphite of a  1:5 μm could fit the flat mid-IR extinction. Again, amorphous carbon is preferred since it requires C/H E72 ppm, less than that of graphite of C/H E 92 ppm. For the RV ¼ 5.5 case, we could not fit the UV/optical/near-IR extinction if we assume the same size distribution for both silicate and graphite. We therefore set ac;S ¼ ac;C , but allow silicate and graphite to have different α values (i.e., αS a αC ). The best-fit results are shown in Fig. 6 and the model parameters are tabulated in Table 1. Similar to the RV ¼3.1 and RV ¼4.0 models, micrometer-sized amorphous carbon and graphite could closely fit the mid-IR extinction, with amorphous carbon being preferred since it does not consume as much C/H as graphite. Finally, we note that it is not clear how micrometer-sized interstellar dust is formed. However, there are several pieces of evidence suggesting its presence in the ISM: (1) measurements by dust impact detectors on the interplanetary spacecrafts Ulysses and Galileo appear to indicate a substantial flux of interstellar particles with masses 4 10  12 g (corresponding to a 40:4 μm for silicate and a 40:5 μm for graphite) entering the heliosphere (see Landgraf et al., 2000; Krüger et al., 2007); (2) Taylor et al. (1996) reported radar detection of a  30 μm particles entering the Earth's atmosphere on solar-hyperbolic trajectories implying that they are arriving from interstellar space. Socrates and Draine (2009) discussed the detectability of very large interstellar grains of a
1 mm (pebble) through optical scattered light halos.

5. Summary The mid-IR extinction curves of a wide variety of interstellar regions (including both diffuse and dense environments) exhibit a

flat or “gray” behavior in the wavelength region of
3–8 μm. This flat mid-IR extinction is hardly accounted for by the standard MRN silicate–graphite dust model. To explain the flat mid-IR extinction, we have considered various dust sizes and species, including amorphous silicate, graphite, amorphous carbon, and iron spheres. we find that micrometer-sized amorphous carbon dust best fits the flat mid-IR extinction. The observed extinction from the UV to the mid-IR could be closely reproduced by a mixture of submicrometer-sized amorphous silicate dust, submicrometersized graphitic dust, and micrometer-sized amorphous carbon dust. However, this mixture requires a solid-phase C abundance of C/H E352 ppm, considerably exceeding what could be available in the ISM.

Acknowledgments We thank J. Gao, A. Mishra, and the anonymous referees for helpful comments/suggestions. We are supported in part by NSFC 11373015 and 11173007, NSF AST-1109039, NASA NNX13AE63G, and the University of Missouri Research Board.

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